Geodesic
On sharp traces of some new analytic Herz-type spaces in Siegel domains in~$\mathbb{C}^n$
Problemy fiziki, matematiki i tehniki, no. 4 (2015), pp. 87-95.

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We provide complete characterizations of traces of some new analytic spaces of Herz-type in polydisk, unit ball and tubular domains over symmetric cones and bounded pseudoconvex domains with smooth boundary under additional natural condition on kernel. Our results extend previously known assertions.
Keywords: analytic functions, Herz-type spaces, polydisk, tubular domains
Mots-clés : pseudoconvex domains. 
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R. F. Shamoyan; O. A. Zaytseva. On sharp traces of some new analytic Herz-type spaces in Siegel domains in~$\mathbb{C}^n$. Problemy fiziki, matematiki i tehniki, no. 4 (2015), pp. 87-95. http://geodesic.mathdoc.fr/item/PFMT_2015_4_a15/

[1] M. Abate, T. Raissy, A. Saracco, “Toeplitz operators and Carleson measures in strongly pseudoconvex domains”, Journal. Funct. Anal., 263 (2012), 3449–3491 | DOI | MR | Zbl

[2] M. Abate, A. Saracco, “Carleson measures and uniformly discrete sequences in strongly pseudoconvex domains”, Journal of London. Math. Soc., 83 (2011), 587–605 | DOI | MR | Zbl

[3] M. Arsenovic, R. Shamoyan, “Trace theorems in harmonic function spaces, multiplier theorems and related estimates”, Kragujevac Math. Journal, 35:3 (2011), 411–430 | MR | Zbl

[4] E. Amar, C. Menini, “A counterexample to the corona theorem for operators in $H^2$ in polydisk”, Pacif. Journal of Mathematics, 206:2 (2002), 257–268 | DOI | MR | Zbl

[5] M. Arsenovic, R. Shamoyan, “On distances and atomic decomposition of Bergman type spaces in pseudoconvex domains with smooth boundary”, Bulletin of Korean Math. Society, 52:1 (2015), 85–105 | DOI | MR

[6] F. Beatrous, “$L^p$ estimates in pseudoconvex domains”, Michigan Math. Journal, 32:3 (1985), 361–380 | DOI | MR | Zbl

[7] D. Bekolle, A. Bonami, G. Garrigos, F. Ricci, B. Sehba, “Analytic Besov spaces and Hardy type inequalities in tube domains over symmetric cones”, Jour. fur. reine und ang., 647 (2010), 25–56 | MR | Zbl

[8] D. Clark, “Restriction of $H^p$ functions in the polydisk”, American Journal of Mathematics, 110 (1988), 1119–1152 | DOI | MR | Zbl

[9] M. Djrbashian, F. Shamoyan, Topics in the theory of Bergman $A_\alpha^p$ spaces, Teubner Texte zur Math., Leipzig, 1988

[10] L. G. Gheorghe, “Interpolation of Besov spaces and applications”, Le Matematiche, LV (2000), 29–42 | MR | Zbl

[11] S. Ishi, S. Yamaji, Some new estimates of Bergman kernel in minimal bounded homogeneous domains, arXiv: 1010.4370

[12] M. Jevtic, M. Pavlovic, R. Shamoyan, “A note on diagonal mapping theorem in spaces of analytic functions in the polydisk”, Publ. Math. Debrechen, 74:1/2 (2009), 1–14 | MR

[13] M. Jevtic, “On $D_\alpha^{p,q}$ spaces”, Mat. Vesnik, 1984

[14] Song-Yong Li, W. Luo, “Analysis on Besov spaces. II: Embedding and Duality Theorems”, Journal of Math. Analysis and Applications, 333:2 (2007), 1189–1202 | DOI | MR

[15] D. Bekolle, A. Bonami, G. Garrigos, C. Nana, M. Peloso, F. Ricci, “Lecture notes on Bergman projectors in tube domain over cones, an analytic and geometric viewpoint”, Proceeding of the International Workshop on Classical Analysis (Yaounde, 2001), 75 | MR | Zbl

[16] D. Bekolle, A. Bonami, G. Garrigos, F. Ricci, Littlewood–Paley decomposition and Besov spaces related to symmetric cones, 2008, 48 pp., arXiv: math/0305072

[17] B. F. Sehba, “Bergman type operators in tube domains over symmetric cones”, Proc. Edinburg. Math. Society, 52, June (2009), 529–544 | DOI | MR | Zbl

[18] B. F. Sehba, “Hankel operators and Shatten classes”, Int. Eq. Op. Th., 2012 | MR

[19] R. Shamoyan, O. Mihic, “On traces of holomorphic functions in polyballs”, Applicable Analysis and Discrete Mathematics, 2009, no. 3, 42–48 | MR | Zbl

[20] R. Shamoyan, O. Mihic, “On traces of $\mathcal{Q}$ type spaces and mixed norm analytic function spaces in polyballs”, Siauliau Math. Seminar, 2010, no. 5(13), 101–119 | MR | Zbl

[21] R. Shamoyan, O. Mihic, “A note on traces of some holomorphic functions classes in polyballs”, Journal of Function Spaces and Applications, 8:3 (2010), 271–285 | DOI | MR | Zbl

[22] R. Shamoyan, O. Mihic, “Sharp trace theorems in Bergman type spaces in pseudoconvex domains”, Doklady NAN Armenii, 114:2 (2014), 91–96 | MR

[23] R. Shamoyan, E. Povpritz, “Sharp trace theorems in Bergman type spaces in tubular domains over symmetric cones”, Journal of Siberian Federal University, 6:4 (2013), 527–538

[24] R. Shamoyan, E. Povpritz, “Sharp Trace theorems in unbounded Siegel domains”, Uzbekistan Math. Journal, 1 (2015), 149–157

[25] R. Shamoyan, S. Li, “On some properties of analytic spaces related with the Bergman metric ball”, Bulletin Iranian Math. Society, 34:2 (2008), 121–139 | MR | Zbl

[26] R. Shamoyan, E. Povpritz, “Embedding theorems and multifunctional analytic spaces in products strongly pseudoconvex domains”, Kragujevac Math. Journal, 37:2 (2013), 221–244 | MR | Zbl

[27] J. Sakai, T. Jimbo, “Interpolation manifolds for products of strictly pseudoconvex domains”, Complex variables and applications, 1997, no. 8, 3–14 | MR | Zbl

[28] S. Yamaji, “Composition operators on the Bergman spaces in minimal domains”, Hiroshima Math. Journal, 43 (2014), 107–127 | MR

[29] K. Zhu, Function theory in the unit ball, Graduate Studies in Math., 2005